Thouless-Anderson-Palmer equations for generic p-spin glasses

Antonio Auffinger, Aukosh Jagannath

Research output: Contribution to journalArticle

Abstract

We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, 〈·〉N, into a mixture of conditional laws, 〈·〉α,N . We show that the TAP equations hold for the spin at any site with respect to 〈·〉α,N simultaneously for all α. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.

Original languageEnglish (US)
Pages (from-to)2230-2256
Number of pages27
JournalAnnals of Probability
Volume47
Issue number4
DOIs
Publication statusPublished - Jan 1 2019

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Keywords

  • Cluster decomposition
  • Random measures
  • Spin glasses
  • TAP
  • Ultrametricity

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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